“Black dwarf supernovae”. They sound quite dramatic! And indeed, they may be the last really exciting events in the Universe.
It’s too early to be sure. There could be plenty of things about astrophysics we don’t understand yet—and intelligent life may throw up surprises even in the very far future. But there’s a nice scenario here:
• M. E. Caplan, Black dwarf supernova in the far future, Monthly Notices of the Royal Astronomical Society 497 (2020), 4357–4362.
First, let me set the stage. What happens in the short run: say, the first 1023 years or so?
For a while, galaxies will keep colliding. These collisions seem to destroy spiral galaxies: they fuse into bigger elliptical galaxies. We can already see this happening here and there—and our own Milky Way may have a near collision with Andromeda in only 3.85 billion years or so, well before the Sun becomes a red giant. If this happens, a bunch of new stars will be born from the shock waves due to colliding interstellar gas.
By 7 billion years we expect that Andromeda and the Milky Way will merge and form a large elliptical galaxy. Unfortunately, elliptical galaxies lack spiral arms, which seem to be a crucial part of the star formation process, so star formation may cease even before the raw materials run out.
Of course, no matter what happens, the birth of new stars must eventually cease, since there’s a limited amount of hydrogen, helium, and other stuff that can undergo fusion.
This means that all the stars will eventually burn out. The longest lived are the red dwarf stars, the smallest stars capable of supporting fusion today, with a mass about 0.08 times that of the Sun. These will run out of hydrogen about 10 trillion years from now, and not be able to burn heavier elements–so then they will slowly cool down.
(I’m deliberately ignoring what intelligent life may do. We can imagine civilizations that develop the ability to control stars, but it’s hard to predict what they’ll do so I’m leaving them out of this story.)
A star becomes a white dwarf—and eventually a black dwarf when it cools—if its core, made of highly compressed matter, has a mass less than 1.4 solar masses. In this case the core can be held up by the ‘electron degeneracy pressure’ caused by the Pauli exclusion principle, which works even at zero temperature. But if the core is heavier than this, it collapses! It becomes a neutron star if it’s between 1.4 and 2 solar masses, and a black hole if it’s more massive.
In about 100 trillion years, all normal star formation processes will have ceased, and the universe will have a population of stars consisting of about 55% white dwarfs, 45% brown dwarfs, and a smaller number of neutron stars and black holes. Star formation will continue at a very slow rate due to collisions between brown and/or white dwarfs.
The black holes will suck up some of the other stars they encounter. This is especially true for the big black holes at the galactic centers, which power radio galaxies if they swallow stars at a sufficiently rapid rate. But most of the stars, as well as interstellar gas and dust, will eventually be hurled into intergalactic space. This happens to a star whenever it accidentally reaches escape velocity through its random encounters with other stars. It’s a slow process, but computer simulations show that about 90% of the mass of the galaxies will eventually ‘boil off’ this way — while the rest becomes a big black hole.
How long will all this take? Well, the white dwarfs will cool to black dwarfs in about 100 quadrillion years, and the galaxies will boil away by about 10 quintillion years. Most planets will have already been knocked off their orbits by then, thanks to random disturbances which gradually take their toll over time. But any that are still orbiting stars will spiral in thanks to gravitational radiation in about 100 quintillion years.
I think the numbers are getting a bit silly. 100 quintillion is 1020, and let’s use scientific notation from now on.
Then what? Well, in about 1023 years the dead stars will actually boil off from the galactic clusters, not just the galaxies, so the clusters will disintegrate. At this point the cosmic background radiation will have cooled to about 10-13 Kelvin, and most things will be at about that temperature unless proton decay or some other such process keeps them warmer.
Okay: so now we have a bunch of isolated black holes, neutron stars, and black dwarfs together with lone planets, asteroids, rocks, dust grains, molecules and atoms of gas, photons and neutrinos, all very close to absolute zero.
I had a dream, which was not all a dream.
The bright sun was extinguishd, and the stars
Did wander darkling in the eternal space,
Rayless, and pathless, and the icy earth
Swung blind and blackening in the moonless air.
— Lord Byron
So what happens next?
We expect that black holes evaporate due to Hawking radiation: a solar-mass one should do so in 1067 years, and a really big one, comparable to the mass of a galaxy, should take about 1099 years. Small objects like planets and asteroids may eventually ‘sublimate’: that is, slowly dissipate by losing atoms due to random processes. I haven’t seen estimates on how long this will take. For larger objects, like neutron stars, this may take a very long time.
But I want to focus on stars lighter than 1.2 solar masses. As I mentioned, these will become white dwarfs held up by their electron degeneracy pressure, and by about 1017 years they will cool down to become very cold black dwarfs. Their cores will crystallize!
Then what? If a proton can decay into other particles, for example a positron and a neutral pion, black dwarfs may slowly shrink away to nothing due to this process, emitting particles as they fade away! Right now we know that the lifetime of the proton to decay via such processes is at least 1032 years. It could be much longer.
But suppose the proton is completely stable. Then what happens? In this scenario, a very slow process of nuclear fusion will slowly turn black dwarfs into iron! It’s called pycnonuclear fusion. The idea is that due to quantum tunneling, nuclei next to each other in the crystal lattice within a black dwarf will occasionally get ‘right on top of each other’ and fuse into heavier nucleus! Since iron-56 is the most stable nucleus, eventually iron will predominate.
Iron is more dense than lighter elements, so as this happens the black dwarf will shrink. It may eventually shrink down to being so dense that electron pressure will no longer hold it up. If this happens, the black dwarf will suddenly collapse, just like heavier stars. It will release a huge amount of energy and explode as gravitational potential energy gets converted into heat. This is a black dwarf supernova.
When will black dwarf supernovae first happen, assuming proton decay or some other unknown processes don’t destroy the black dwarfs first?
This is what Matt Caplan calculated:
We now consider the evolution of a white dwarf toward an iron black dwarf and the circumstances that result in collapse. Going beyond the simple order of magnitude estimates of Dyson (1979), we know pycnonuclear fusion rates are strongly dependent on density so they are greatest in the core of the black dwarf and slowest at the surface. Therefore, the internal structure of a black dwarf evolving toward collapse can be thought of as an astronomically slowly moving ‘burning’ front growing outward from the core toward the surface. This burning front grows outward much more slowly than any hydrodynamical or nuclear timescale, and the star remains at approximately zero temperature for this phase. Furthermore, in contrast to traditional thermonuclear stellar burning, the later reactions with higher Z parents take significantly longer due to the larger tunneling barriers for fusion.
Here “later reactions with higher Z parents” means fusion reactions involving heavier nuclei. The very last step, for example, is when two silicon nuclei fuse to form a nucleus of iron. In an ordinary star these later reactions happen much faster than those involving light nuclei, but for black dwarfs this pattern is reversed—and everything happens at ridiculously slow rate, at a temperature near absolute zero.
He estimates a black dwarf of 1.24 solar masses will collapse and go supernova after about 101600 years, when roughly half its mass has turned to iron.
Lighter ones will take much longer. A black dwarf of 1.16 solar masses could take 1032000 years to go supernova.
These black dwarf supernovae could be the last really energetic events in the Universe.
It’s downright scary to think how far apart these black dwarfs will be when they explode. As I mentioned, galaxies and clusters will have long since have boiled away, so every black dwarf will be completely alone in the depths of space. Distances between them will be doubling every 12 billion years according to the current standard model of cosmology, the ΛCDM model. But 12 billion years is peanuts compared to the time scales I’m talking about now!
So, by the time black dwarfs start to explode, the distances between these stars will be expanded by a factor of roughly
compared to their distances today. That’s a very rough estimate, but it means that each black dwarf supernova will be living in its own separate world.